1. Technical Field
Embodiments of the subject matter disclosed herein generally relate to methods and devices used for processing seismic data and, more particularly, to generating models of signal and/or noise using data-domain weights based on estimated signal-to-noise ratios.
2. Discussion of the Background
Seismic data related to energy reflected from interfaces between geological layers of an explored subsurface structure are used in the oil and gas industry to search for and evaluate subterranean hydrocarbon deposits. After seismic waves are injected into the explored underground structure, seismic receivers detect the reflected energy (a signal, which may be coherent with the injected waves), and undesirable noise. Various methods are employed to attenuate or remove noise from the seismic data.
Noise, which is characterized by amplitude and/or phase, can be transformed (as can the signal and seismic data in general) to different domains (space-time domain, frequency domain, etc.). Some of the noise is predictable and coherent with the signal in some domains, while unpredictable and incoherent with the signal in other domains. Noise that is random and unpredictable, or whose predictability has been altered by transforming the data to a particular domain (for example, by sorting) may be easier to remove without altering the coherent signal. Noise that is coherent in one domain but incoherent in another may be attenuated using methods for removing incoherent noise, applied in the domain in which the noise is incoherent. The denoised data may then be sorted back to the domain in which the noise was coherent.
Unpredictable noise can be attenuated using frequency-space filtering (as described, e.g., in the article, “Random noise reduction,” by Canales, L., published in 54th SEG Annual International Meeting 1984, Expanded Abstracts, pp. 525-527; the article, “Signal-preserving random noise attenuation by the F-X projection,” by Soubaras, R., published in 64th SEG Annual International Meeting 1994, Expanded Abstracts, pp. 1,576-1,579; or the article, “Coherency enhancement on 3D seismic data by dip detection and dip selection,” by Gulunay et al., published in 77th SEG Annual International Meeting 2007, Expanded Abstracts, pp. 2,247-2,251, the entire contents of which are incorporated herein by reference). This technique, which can be applied in one or more spatial dimensions in which noise is incoherent, relies on a prediction of the coherent signal at a point in space using surrounding traces on which the noise is sufficiently random as to average out to zero (or close to zero). Such randomness is achieved with large enough collections of data in which the noise has a normal probability distribution. However, when the noise on surrounding traces is particularly strong, or is not truly random, prediction of the coherent signal and, consequently, of the noise is compromised. Hence, the technique is inefficient in the presence of high-density and strong noise, or types of noises that are not truly random in amplitude or phase. Furthermore, this technique is accurate only for data that is regularly distributed in the spatial dimensions in which it is processed (e.g., regular shot and receiver spacing), and for data that is not aliased.
Strong incoherent noise occurs, for example, when data is acquired such that the interval between shots (i.e., seismic sources' activation to generate seismic waves incident on the explored formation) is shorter than the recording (“listening”) period corresponding to one shot. In this case (which is known as “simultaneous source acquisition”), the acquired seismic data is blended, including overlapping signals caused by incident waves from different but simultaneously shot sources. The later signal, cross-talk interference and other noise are generally not coherent with the earlier shot and resulting earlier signal in one or more domains, but constitute a strong noise for the earlier signal (and vice-versa, the earlier signal, cross-talk and other noise are generally not coherent with the later shot and resulting later signal, constituting a strong noise for the later signal in an appropriate domain).
Simultaneous source acquisition is desirable because it reduces a survey's total acquisition time and cost, or it may be used to acquire a higher density dataset in the same survey time. Simultaneous source acquisition can be performed in land and marine environments (with ocean bottom receivers or towed streamers), with continuous or non-continuous recording. Using blended data requires additional processing to extract seismic datasets focusing on individual signals (i.e., deblending the data).
In conventional surveying techniques, sources are activated so that a signal corresponding to one shot does not overlap another signal corresponding to another shot in their significant portions (e.g., when the signal amplitudes are substantially greater than the noise). FIG. 1A illustrates seismic waves generated at different spatial positions 10, 12 and 14 at intervals so the recorded wavelets 10a-c corresponding to the seismic waves generated at spatial position 10 do not interfere with wavelets 12a-c corresponding to the seismic waves generated at spatial position 12. The wavelets generated due to one shot form a signal carrying information about the explored underground structure.
The receivers may record continuously in time (i.e., 16 in FIG. 1A) or separately to form regular seismic traces for each individual shot, as shown in FIG. 1B. The traces illustrated in FIG. 1B form a receiver gather 20. First wavelets, which correspond to reflections from a first interface, form curve a, second wavelets form curve b, etc.
FIG. 2A illustrates seismic waves generated at the same positions as in FIG. 1A, but at shorter intervals so the corresponding recording times partially overlap. Therefore, for example, wavelet 10c overlaps wavelet 12a. FIG. 2B shows receiver gather 30 formed with regular seismic traces extracted from continuous recording based on each shot's start time. FIG. 2B data has been acquired in less time than FIG. 1B data. Cross-talk like 32, which appears to be noise on the traces, is in fact a signal wavelet of another trace. When simultaneous source acquisition is used, it is necessary to separate (deblend) the energy (wavelets) associated with each shot as a pre-processing step.
In land simultaneous source acquisition, a variety of different sources (for example, different vibroseis sweeps or pseudo-random sweeps) yielding different signatures are used to ease separation of blended data. When energy from a given shot is time-aligned, a source designature operator for that shot can be applied to focus the energy related to that shot while keeping energy from other shots dispersed.
In marine acquisition, the sources' firing time (as described in the article, “A Universal Simultaneous Shooting Technique,” by DeKok et al., EAGE 64th Conference & Exhibition 2002, the entire content of which is incorporated herein by reference) is used as a key for deblending the data. Most deblending algorithms rely on the randomness of the firing time, using denoising or sparseness constraints that make the energy separable.
Varying shot timing (known as “timing dither”), which is seismic source activations at varying intervals, yields an incoherency in cross-talk noise timing in domains other than the shot domain. For example, FIG. 3 (corresponding to Hampson et al., “Acquisition using simultaneous sources,” Leading Edge, Vol. 27, No. 7, the entire content of which is incorporated herein by reference) is a sequence of graphs representing the same blended seismic data in different domains: common shot, common receiver, common midpoint and common offset.
Traditionally, datasets focusing on an individual signal are extracted from blended data using methods that fall into the following categories (all relying to some degree on randomized timing):
1. Separation in a model domain,
2. Impulsive denoising,
3. Iterative coherency enhancement/denoising, and
4. Full modeling of energy from all sources.
Separation in a model domain may be used when the energy coming from different sources can be separated through muting in a model domain. For example, one such method (described in the article, “Fast and robust deblending using Apex Shifted Radon transform,” by Trad et al., published in SEG Expanded Abstracts 2012, the entire content of which is incorporated herein by reference) uses an apex shifted Radon to separate cross-talk noise.
Impulsive denoising technique (disclosed, for example, in the article, “Acquisition using simultaneous sources,” by Stefani et al., published in 69th EAGE Conference & Exhibition, 2007, the entire content of which is incorporated herein by reference) uses the fact that when data is sorted into any domain other than the common shot, the cross-talk noise from other sources is incoherent, as illustrated in FIG. 3 (corresponding to the previously referred-to article of Hampson et al.). Note that in the common shot domain, cross-talk noise 40 is continuous. Variable firing times allow the use of impulsive-noise attenuation techniques that are already available and used in other processing steps, such as swell-noise attenuation. While this method can effectively remove the strongest cross-talk energy, low-amplitude cross-talk noise is not seen as impulsive and will not be removed.
Iterative coherency enhancement/denoising techniques (described, for example, in U.S. Pat. No. 6,882,938, in the article, “Iterative method for the separation of blended seismic data: discussion on the algorithmic aspects” by A. Mahad et al., published in Geological Prospecting, 2012, 60, pp. 782-801, in the article, “Separating simultaneous sources by inversion,” by Abma et al., published in 71st EAGE Conference & Exhibition, 2009; the article, “Source Separation by Iterative Rank Reduction—Theory and Applications,” by M. Maraschini et al., published in 74th EAGE Conference & Exhibition, 2012; and the article, “An iterative SVD method for deblending: theory and examples,” by M. Maraschini et al., published in SEG Technical Program Expanded Abstracts 2012, the entire contents of which are incorporated herein by reference) rely on the fact that cross-talk noise on some traces is a duplication of signal on other traces. This means that with knowledge of the timing of all shots, a signal estimate made for one source can then be used to reduce the level of cross-talk for all other sources.
The full modeling of energy from all sources technique (described, for example, in the article, “Simultaneous source separation by sparse Radon transform,” by Akerberg et al., published in 78th Ann. Internat. Mtg.: Soc. of Expl. Geophys, 2008; and the article, “Simultaneous source separation using dithered sources,” by Moore et al., published in 78th Ann. Internat. Mtg.: Soc. of Expl. Geophys, 2008, the entire contents of which are incorporated herein by reference) has similarities to the iterative denoising method, except that this formulation solves the relationship between source energy and cross-talk noise implicitly at the core of the problem formulation. Equations can be formulated as designing a transform domain for each source or spatial area (e.g., tau-p domain, Fourier domain, etc.) such that when it is reverse-transformed and reblended, the raw input data is reconstructed as accurately as possible in a least squares sense.
This technique (i.e., full modeling of energy from all sources) uses the timings and positioning of all sources and also relies on a sparse solution to the equations. Once the transform domains have been calculated, the final step to deblend the data requires application of reverse-transform without reblending. While this method may result in some filtering of the original data, it removes low-amplitude cross-talk noise and preserves the primary signal. This method could be considered an alternative way to solve the same problem as the iterative coherency enhancement/denoising technique (analogous to sparse least squares Radon versus inversion through “iterative cleaning”).
It is, however, desirable to develop denoising methods able to extract coherent signal from strong and/or high-density noise, or noise that is not fully random.